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counting stable sets recursively...need help

Given a linked list tree, where A is the root, with 2 children B and C. And B has two children D and E, such that A->[B->C] C->[D->E] . In this case, there are 14 stable sets. A stable set is a possibly empty subset, S, of the vertices such that no two nodes in S are adjacent to each other in the tree.